### Theory Weekly Highlights for January 2014

##### January 31, 2014

A new transport model that uses neural networks (NNs) to yield electron and ion heat flux profiles has been developed. Given a similar set of local dimensionless plasma parameters that the highest fidelity models use, the NN model is able to efficiently and accurately predict the heat transport profiles. As a benchmark, a NN was built, trained, and tested on data from the 2012 and 2013 DIII-D experimental campaigns. Results show that the NN can capture the experimental behavior over the majority of the plasma radius and across a broad range of plasma regimes. Although in the model each radial location is calculated independently from the others, the heat flux profiles are smooth, suggesting that the solution found by the NN is a smooth function of the input parameters, which supports the evidence of a well-defined, non-stochastic relationship between the input parameters and the transport fluxes. The numerical efficiency of this method makes the NN approach an ideal candidate for scenario development simulations and real-time plasma control.

##### January 24, 2013

The effects of non-axisymmetry on neoclassical flows and transport have been explored using a new 3D extension of NEO that retains all of the 2D physics features of NEO in the diamagnetic ordering limit. NEO is coupled directly with the new 3D local equilibrium solver LE3 for fast 3D shaping studies. Neoclassical toroidal viscosity (NTV) with full kinetic dynamics, as well as the non-ambipolar particle fluxes, has been verified. Results including kinetic electrons with full collisional coupling have identified new physically interesting collisionality regimes of 3D transport. At high collisionality, the Pfirsch-Schluter particle flux, Γi, nearly recovers the 2D axisymmetric ambipolar (Γi = Γe) ν* scaling since collisions, rather than the non-axisymmetry, dominate the dynamics. As the collisionality decreases, the ions and electron transport enters a plateau-like regime and then one obtains the strongly enhanced 1/ν* transport at low collisionality, for the ions, and at lower collisionality values for the electrons, reduced by roughly the square root of the electron to ion mass ratio. The 1/ν* divergence is clearly unphysical, and points to a breakdown of the drift ordering in the limit of very weak collisions. In this limit, we expect the transport to approach a finite limiting value determined by stochastic motion of the particles in the nonaxisymmetric field.

##### January 17, 2013

The Trapped Gyro-Landau Fluid (TGLF) quasilinear model is now able to predict the electron density, electron and ion temperatures and ion toroidal rotation simultaneously for internal transport barrier (ITB) discharges that satisfy the high-ExB velocity ordering, in excellent agreement with data from the DIII-D tokamak. Inside the ITB, the ion energy transport is reduced to the neoclassical level, which is consistent with the theory of turbulence suppression by ExB velocity shear acting on low wavenumber turbulence. The electron energy transport is observed to be far above the neoclassical level, consistent with electron energy transport due to high wavenumber electron temperature gradient (ETG) modes. The key to predicting ITB transport is the inclusion of ion gyro-radius scale modes that become dominant at high ExB shear, and to recent improvements to TGLF that allow the Kelvin-Helmholtz (KH) mode, which arrests the suppression of transport by the shear in the ExB velocity Doppler shift at high toroidal flow shear, to be faithfully modeled.

##### January 10, 2013

A resistive wall model has been implemented in M3D-C1, in which the both the resistive wall and the region external to the vessel are included within the computational domain. This method is expected to have several advantages over the method in which the resistive wall is implemented as a boundary condition, including improved parallel scalability and the ability to treat the resistivity and temperature of the wall as functions of time and space. Although the geometry of the wall is axisymmetric, non-axisymmetric variations in its resistivity may be included to model ports and TBMs, for example. Initial calculations in NSTX geometry have confirmed the ability to model resistive wall modes. This new capability will allow the calculation of resistive wall modes, vertical instabilities, and free-boundary plasma response with M3D-C1.

**Disclaimer**

These highlights are reports of research work in progress and are accordingly subject to change or modification